A good way to represent negative numbers and products is with money owed, or IOUs.
Let's say you owe a friend $20. If you owe two friends, you owe $40, or, you have -$40. And so forth. You can represent the second one by multiplying 2(-20) = -40
For our problem, the product would be 8 * -20 = -160. A situation for this is that you have eight friends and you each friend $20. In total you owe $160, or have -$160.